Efficiency non-self tuning wireless power transfer systems

ABSTRACT

A primary resonant network for a wireless power transfer has a primary winding capable of being energised to provide a magnetic field, and a reactive component selected to constrain the reactive loading on a power supply which energises the primary resonant network. The reactive component is selected dependent on a given variation in inductance or capacitance of the primary resonant network and a given variation in inductance or capacitance of a secondary resonant network coupled to the primary resonant network.

This invention relates to wireless power transfer systems, also known asinductive power transfer (IPT) systems.

BACKGROUND TO THE INVENTION

Inductive Power Transfer (IPT) systems are, well known. An example ofone such system is shown generally in FIG. 1. Such systems are alsodescribed comprehensively in the prior art, including for example U.S.Pat. No. 5,293,308.

In recent times IPT systems have been used in electric vehicle batterycharging applications. A significant advantage of IPT for electricvehicle battery charging is its tolerance to misalignment between theprimary magnetic structure and the magnetic structure of the secondary(also referred to in this document as a pick-up) apparatus. As shown inFIG. 1, an IPT charger typically includes a switching power supply suchas a resonant converter which is supplied from a utility grid and inturn provides an alternating current to a primary inductor which maycomprise a track or a magnetic structure in the form of a pad forexample. The varying magnetic field which is provided by the primary padis then intercepted by one or more secondary magnetic structures whichusually comprise a further pad or coil, represented in FIG. 1 byinductance L2. The power received is conditioned by a resonant networkand power controller in the pick-up apparatus and then supplied to theelectrical load, for example a battery, being charged.

Physical movement or displacement between the ferrimagnetic material andcoils in the pick-up (L2) relative to the primary pad (L1) necessarilyintroduces variations in the magnetic coupling between the pads and alsointroduces variations in the pad self inductance. Also, variations inthe tuning generally in IPT systems can change dependent on otherfactors, for example component tolerances and variations over time (e.g.tuning capacitor degradation), breakage of ferrite in magneticstructures, etc. Therefore, it is impossible for both the primary andsecondary charging pads to always be accurately tuned over given rangeof movement within a specified power transfer zone without adoptingself-tuning circuitry. In a fixed frequency primary side currentcontrolled system, this places additional reactive load on the powersupply, although it does not affect the power transfer capability of thepick-up providing the track current can be regulated at a desiredmagnitude. However, the mistuned resonant network introduces additionalreactive load in the system and this reactive load increases the lossesin the system

in general, including the power supply, additional switch conductionloss and losses in the magnetic coupling structures. Therefore, creatingsystems in which the reactive load due to mistuning is minimised isadvantageous.

OBJECT

It is an object of the present invention to provide IPT systems andapparatus and methods of IPT system and apparatus design which will atleast go some way toward overcoming one or more disadvantages of theprior art, or which will at least provide a useful alternative.

SUMMARY OF THE INVENTION

Accordingly in one aspect the invention broadly consists in a wirelesspower transfer primary network and/or secondary in which one or morecomponents are selected dependent on the due to variation in the tuningof the primary and/or secondary resonant networks and/or variationcoupling between the primary network and secondary networks.

In one embodiment the one or more components are selected to minimisereactive loading seen by the primary power supply.

In another embodiment the one or more components are selected tominimise the displacement power factor seen by the primary power supply.

In another embodiment the one or more components are selected tominimise the current in the secondary primary network. Preferably theload seen by the primary power supply is inductive over a nominal loadrange.

In another aspect the invention broadly provides a wireless powertransfer primary resonant network including:

a primary winding capable of being energised to provide a magneticfield;at least one reactive tuning component selected to constrain thereactive loading on a power supply which energises the primary resonantnetwork, the reactive tuning component being selected dependent on agiven variation in inductance or capacitance of the primary resonantnetwork and a given variation in inductance or capacitance of asecondary resonant network coupled to the primary resonant network.

The reactive tuning component may be selected dependent on a givenvariation in coupling between the primary and secondary resonantnetworks.

The reactive tuning component may be selected to constrain the variationin reactive loading on the power supply.

The reactive tuning component may be selected to constrain the powerfactor.

In one embodiment the tuning component comprises the primary winding.

The given variation in inductance or capacitance may be caused byrelative movement or displacement of a pick-up winding of the secondaryresonant network relative to the primary winding.

The given variation in coupling may be caused by relative movement ordisplacement of a pick-up winding of the secondary resonant networkrelative to the primary winding.

In another aspect the invention broadly provides a wireless powertransfer secondary resonant network including:

a pick-up winding capable of receiving energy from a varying magneticfield produced by a primary resonant network;at least one reactive tuning component selected to constrain thereactive loading on a power supply which energises the primary resonantnetwork, the reactive tuning component being selected dependent on agiven variation in inductance or capacitance of the secondary resonantnetwork and a given variation in inductance or capacitance of theprimary resonant network to which the secondary resonant network iscoupled.

The reactive tuning component may be selected dependent on a givenvariation in coupling between the primary and secondary resonantnetworks.

The reactive tuning component may also be selected to constrain thevariation in reactive loading on the power supply.

The reactive tuning component may be selected to constrain the powerfactor.

The tuning component may comprise the pick-up winding.

In one embodiment the given variation in inductance or capacitance iscaused by relative movement of the pick-up winding relative to a primarywinding of the primary resonant network.

In one embodiment the given variation in coupling is caused by relativemovement or displacement of the pick-up winding the pick-up windingrelative to a primary winding of the primary resonant network.

In another aspect the invention broadly provides apparatus for wirelesspower transfer including:

a primary resonant network,a secondary resonant network coupled to the primary resonant network,wherein the wireless power transfer system has a system operatingfrequency and one or both of the primary resonant network and thesecondary resonant network have a natural resonant operating frequencythat is different from the system operating frequency, andwherein the natural resonant operating frequency of the primary resonantnetwork is selected dependent on a given variation in inductance orcapacitance of the primary resonant network and a given variation ininductance or capacitance of the secondary resonant network.

In one embodiment the natural resonant operating frequency of theprimary resonant network is selected dependent on a given variation incoupling between the primary and secondary resonant networks.

In one embodiment the natural resonant operating frequency of theprimary resonant network is selected to constrain a variation in theoperating frequency of the primary resonant network.

In another aspect the invention broadly consists in a method ofdesigning a wireless power transfer primary network and/or power supplyand/or pick-up comprising selecting one or more components dependent onthe variation in the tuning of the primary and/or secondary resonantnetworks and variation in coupling between the primary network and thesecondary network.

In one embodiment the one or more components are selected to minimisereactive loading on the power supply.

In another embodiment the one or more components are selected tominimise the displacement power factor seen by the primary power supply.

In another embodiment the one or more components are selected tominimise the current in the primary network. Preferably the load seen bythe primary power supply is inductive over a nominal load range.

In another embodiment the one or more components are selected tominimise the current in the secondary. Preferably the load seen by theprimary power supply inverter is inductive over a nominal load range.

In another aspect the invention broadly provides a wireless powertransfer primary resonant network wherein the nominal inductance of thenetwork is selected such that the change in the total reactive load ofthe network is minimised within a defined range of relative movementbetween a magnetic structure of the primary and a magnetic structure ofa pick-up device.

In one embodiment the nominal inductance is selected such that the inputimpedance to the network is not capacitive.

In one embodiment the nominal inductance is selected such that the inputimpedance to the network is inductive. Preferably the input impedance ismaintained inductive over the operating parameters of the system.

In another aspect the invention broadly provides a wireless powertransfer pick-up wherein the nominal inductance of the pick-up isselected such that the change in the total reactive load of a primaryresonant network from which the pick-up receives power in use isminimised within a defined range of relative movement between a magneticstructure of the primary network and a magnetic structure of a pick-updevice.

In another aspect the invention provides apparatus for wireless powertransfer wherein the nominal inductance of the primary resonant networkand the nominal inductance of a pick-up are selected such that thechange in the total reactive load of a primary resonant network fromwhich the pick-up receives power in use is minimised within a definedrange of relative movement between a magnetic structure of the primarynetwork and a magnetic structure of the pick-up.

In another aspect the invention provides a method of designing awireless power primary resonant network comprising selecting the nominalinductance of the network such that the change in the total reactiveload of the network is minimised within a defined range of relativemovement between a magnetic structure of the primary and a magneticstructure of a pick-up device.

In yet another aspect the invention provides a method of designing awireless power transfer pick-up comprising selecting the nominalinductance of the pick-up such that the change in the total reactiveload of a primary resonant network from which the pick-up receives powerin use is minimised within a defined range of relative movement betweena magnetic structure of the primary network and a magnetic structure ofa pick-up device.

In yet another aspect the invention provides a method of designingwireless power transfer apparatus comprising the steps of selecting thenominal inductance of the primary resonant network and the nominalinductance of a pick-up such that the change in the total reactive loadof a primary resonant

network from which the pick-up receives power in use is minimised withina defined range of relative movement between a magnetic structure of theprimary network and a magnetic structure of the pick-up.

The variations in coupling may be variations in reactive load thatappear to be inductive or capacitive.

The mistuning or variations in tuning may be mistuning or variations inreactive load that appear to be inductive or capacitive.

The variations in coupling may occur due to one or more of:

Changes in physical position of one or more pick-up devices relative toa track or a lumped primary structure;

Use of different pick-up magnetic structures;

Changes in the componentry or magnetics, such as damaged ferrite.

The mistuning or variations in tuning may occur due to one or more of:

Component tolerances;

Manufacturing tolerances;

Component degradation or other changes.

In a further aspect the invention broadly consists in any novel feature,or method step, or any novel combination of features or method stepsdisclosed herein.

Further aspects of the invention, which should be considered in all itsnovel aspects, will become apparent from the following description.

DRAWING DESCRIPTION

One or more embodiments will be described further below with referenceto the accompanying drawings, in which:

DRAWING DESCRIPTION

FIG. 1 is a schematic of a known IPT system;

FIG. 2 is a circuit diagram of the fundamental structure of commonwireless battery charging system which is referred to by way of exampleto describe the invention with reference to further drawings below.

FIG. 3 a is an equivalent AC resistive load of a full bridge dioderectifier with capacitor output filter for series tuned and LCL tunedpick ups.

FIG. 3 b is an equivalent AC resistive load of a full bridge dioderectifier with inductor output filter for parallel tuned pick ups.

FIG. 4 is a conceptual diagram of a mistuned series tuned pick up. Inthis Figure both L₂₀ and ΔL₂ are coupled with L₁.

FIG. 5 is a conceptual diagram of a mistuned parallel tuned pick up.

FIG. 6 is a conceptual diagram of the primary LCL network load moulding.

FIG. 7 is a graph showing track current variation against pick up tuningnetwork variation for various values of Q₂₀.

FIGS. 8 a to 8 c are flow charts showing various design processes forcreating IPT systems or IPT system components according to theinvention.

FIG. 9 is a diagram showing the structure of a 1.2 kilowatt batterycharging system with equivalent AC resistor load at the pick up output.

FIG. 10 is a conceptual diagram of the various positions for maximumcoupling at position A and minimum coupling at position B being thegiven variation in relative position for a coupled primary pad andsecondary pad.

FIGS. 11 a to 11 f show measurements of a 700 mm circular charging padfor changes in the x direction at a z axis direction of 100 mm and 150mm.

FIG. 11 a shows measured bi-filar pad inductance with its magneticallycoupled pad open circuited and short circuited for variations in x(millimetres) at (a) z=100 millimetres and (b) z=150 millimetres.

FIGS. 11 c and d show measured single wire pad inductances withmagnetically coupled pad open circuited for variations in x(millimetres) at (c) z=100 millimetres and (d) z=150 millimetres.

FIGS. 11 e and f show measured mutual inductance between a bi-filarwound pad and a single wire wound pad for variations in x (millimetres)at (e) z=150 millimetres and (f) z=150 millimetres.

FIG. 12 shows plots representing analytical results of the primary LCLnetwork with 700 millimetre circular pad and series tuned pick up tunedat position AA, BB and the new tuning design against changes in x atz=100 millimetres and z=150 millimetres.

FIG. 12 a shows pick up reflected equivalent inductance L_(R) versuschanges in x (millimetres) at (A) z=100 millimetres and (B) z=150millimetres.

FIGS. 12 c and 12 d show the equivalent primary inductance L₁ equiv forchanges in x (millimetres) at (c) z=150 millimetres, and (d) z=150millimetres.

FIGS. 12 e and f show the ratio of LCL input reactants over resistanceagainst distance x (millimetres) at (e) z=100 millimetres and (f) z=150millimetres.

FIGS. 12 g and h show the primary LCL network input displacement powerfactor against x (millimetres) at (g) z=100 millimetres and (h) z=150millimetres.

FIG. 13 shows analytical and SPICE simulation results of the primary LCLnetwork with the 700 millimetre circular pad and series tuned pick uptuned at the new tuning values against changes in x, at z of 100millimetres and 150 millimetres.

FIGS. 12 a and 12 b show pick up reflected equivalent inductance L_(R)against x (millimetres) at (a) z=100 millimetres and (b) z=150millimetres.

FIGS. 13 c and d show the ratio of LCL input reactance over resistanceagainst changes in x (millimetres) at (c) z=100 millimetres and (d)z=150 millimetres.

FIGS. 13 e and f show the primary LCL network input displacement powerfactor against changes in x (millimetres) at (e) z=100 millimetres and(f) z=150 millimetres.

FIG. 14 shows the analytical results of the primary LCL network with 700millimetre circular pad and parallel tuned pick up positioned atposition AA, BB at the new tuning value against changes in x at z=100millimetres and 150 millimetres.

FIG. 14 a shows the pick up reflected equivalent inductance L_(R) versuschanges in x (millimetres) at (a) z=100 millimetres and (b) z=150millimetres.

FIGS. 14 c and d show the equivalent primary inductance L₁ equiv versuschanges in x (millimetres) at (c) z=100 millimetres and (d) z=150millimetres.

FIGS. 14 e and f show the ratio of LCL input reactance over resistanceagainst changes in x (millimetres) at (e) z=100 millimetres and (f)z=150 millimetres.

FIGS. 14 g and h show the primary LCL network input displacement powerfactor against changes in x (millimetres) at (g) 100 millimetres and (h)z=150 millimetres.

FIG. 15 shows the analytical and SPICE simulation results of the primaryLCL network with 700 millimetre circular pad and parallel tuned pick uptuned at the new pick up values against x at z of 100 millimetres and150 millimetres.

FIGS. 15 a and b show the pick up reflected equivalent inductance L_(R)against x (millimetres) at (a) z=100 millimetres and (b) z=150millimetres.

FIGS. 15 c and d show the ratio of LCL input reactance over resistanceagainst changes in the x (millimetres) at (c) z=100 millimetres and (d)z=150 millimetres.

FIGS. 15 e and f show the primary LCL network input displacement powerfactor against changes in x (millimetres) at (e) z=100 millimetres and(f) z=150 millimetres.

FIG. 16 shows SPICE simulation results with the fundamental component ofthe primary inverter bridge voltage V_(B1) and current I_(B1) with 700millimetre circular pad with series tuned and parallel pick up using thedeveloped tuning technology against changes in the x z of 100millimetres and 150 millimetres.

FIGS. 16 a and b show the fundamental component of an inverter bridgevoltage against changes in x (millimetres) at (a) z=100 millimetres and(b) z=150 millimetres.

FIGS. 16 c and 16 d show the fundamental component of an inverter bridgecurrent against changes in x (millimetres) at (c) z=100 millimetres and(d) z=150 millimetres.

FIG. 17 is a conceptual diagram showing a constraint in movement over acoupling area which may be applied to magnetic structures of othershapes.

FIGS. 18 to 26 generally show changes in frequency of primary andsecondary coupled resonant networks for a system having an operatingfrequency of 20 khz for various tuning arrangements when the secondarypad is moved from a coupling position of maximum coupling (a) to minimumcoupling (b) within a defined power transfer area as described withreference to FIG. 10.

FIG. 18 relates to a series tuned pick up with the system tuned in theAA position.

FIG. 19 relates to a series tuned LC pick up with the system tuned inthe BB position.

FIG. 20 relates to a series LC tuned pick up with the system tuned at ABposition, the pick up tuned with B position inductance the primary tunedwith A position inductance.

FIG. 21 relates to a series tuned LC pick up with a system tunedaccording to a new design.

FIG. 22 relates to a parallel tuned LC pick up, with a system beingtuned in the AA position.

FIG. 23 relates to a parallel tuned LC pick up with a system being tunedin the BB position.

FIG. 24 relates to a parallel tuned LC pick up, with a system beingtuned according to a new design.

FIG. 25 shows an example of using a design described herein to minimiseVA₁ and VA₂ individually.

FIG. 26 shows examples of adjusting the VA₂ variation to assistminimising the VA₁ variation according to the invention.

DETAILED DESCRIPTION

As discussed in the background section above, in practise variouschanges in the resonant network of the primary resonant system and thesecondary (or pickup) resonant system mean that the resonant networksfor the primary and secondary become mistuned. Typically, a wirelesspower transfer system has an operating frequency which may be designatedω_(o.) This operating frequency is typically the frequency of which theprimary side power supply will energise the primary resonant network.However, when mistuning occurs, the resonant frequency under operatingconditions for the primary and secondary resonant networks changes. Inthis document, the natural resonant operating frequency for the primaryside is designated as ω₁ and the natural resonant operating frequencyfor the secondary resonant network is referred to is ω₂. As describedabove, the mistuning can be due to a number of factors such as changesand reactive component values over time, through degradation forexample; manufacturing tolerances for the reactive components such asmagnetic structures which are used to generate or receive fields forpower transfer; manufacturing tolerances and tuning capacitors;self-inductance of the magnetic structures due to changes in relativeposition of the structures. These changes are quite distinct fromvariations in the load connected to the output of the secondary, beingthe load which the IPT system supplies with power.

Traditionally, in the design of wireless power transfer systems,particularly those in which there are “lumped” primary and secondarycoils (i.e. a distinct winding on the primary side and a correspondingdistinct, but not necessarily identical, winding on the secondary side)the standard approach in design has simply been to tune the primary andsecondary resonant circuits at a known fixed relative displacement fromeach other. Usually the known relative position is either at the closestand most centrally located position within a defined space, or thefurthest position within the defined operating space. Thus, referring toFIG. 10, when the secondary pad 12 is located at position A relative tothe primary pad 10, then that corresponds to the closest position withina defined operating area which extends in a 100 mm from the centre ofthe primary pad and up to 150 mm in a vertical direction above theprimary pad. When the secondary pad 12 is in a position as shown in FIG.10, at point B the two pads are at the furthest relative position fromeach other within the defined operating area. Reference in this documentto an IPT system or a wireless power transfer system pad means eitherthe winding, or the complete magnetic structure which includes thewinding is part of the primary and/or secondary resonant network whichis used to transfer power inductively.

The approach to design described in the document is applicable towireless or IPT systems that use a track and multiple pick-ups, as wellas lumped systems. It is also applicable to different types of pick-up,for example “DDQ” and “Bipolar” pick-up structures such as thosedisclosed in international patent publications WO2011/016737 andWO2010/090539, the contents of which are incorporated herein byreference. Furthermore, those skilled in the art will appreciate that itcan be applied to bi-directional systems.The variations in coupling may be variations in reactive load thatappear to be inductive or capacitive. The mistuning or variations intuning may be mistuning or variations in reactive load that appear to beinductive or capacitive.For example, the variations in coupling may occur due to one or more of:Changes in physical position of one or more pick-up devices relative toa track or a lumped primary structure;Use of different pick-up magnetic structures, such as circular pick-ups,DDQ pick-ups and bipolar pick-ups.The mistuning or variations in tuning may occur due to one or more of:Component tolerances;Manufacturing tolerances;Component degradation, such as degradation of tuning capacitors overtime, or other changes.Changes in the componentry or magnetics, such as damaged ferrite.This initial design does not elaborate on a method of minimisingreactive power in the pick-up coil. This design emphasises minimisingthe reactive load in the inverter bridge. It also does not discussminimising I1. These aspects are discussed further in other parts ofthis document.

Fundamental Structure of a Lumped Coil Battery Charging System

The most common industrial IPT power supply topology is the full bridgevoltage-sourced inverter with a series-parallel LCL resonant network. Ifonly the fundamental frequency is considered, a conceptualrepresentation of the power supply with a coupled pick-up is illustratedin FIG. 2 where the inverter bridge output is represented by itsfundamental voltage component V_(B) _(—) ₁. In some cases a capacitorC_(L1), in series with the primary track inductor L₁, is used topartially compensate L₁ to have a total reactance of X, the designedcharacteristic impedance of the primary LCL network. In a primary sidecurrent control system, minimal control is required in the pick-up so itconsists of only the bridge rectifier and a DC filter. The track currentis directly controlled by the fundamental component of the inputinverter bridge voltage V_(B) _(—) ₁ as given in (1).

$\begin{matrix}{I_{1} = \frac{V_{B_{—}1}}{X}} & (1)\end{matrix}$

The three most common pick-up tuning topologies are series-tuned,parallel-tuned and LCL tuned topologies. Considering only thefundamental frequency, the pick-up can be modelled as an LCR circuitusing an equivalent AC resistive load to represent the DC load as shownin FIG. 3. This equivalent AC resistive load for a series tuned or LCLtuned pick-up is given by:

$\begin{matrix}{R_{AC} = {\frac{8}{\pi^{2}}R_{DC}}} & (2)\end{matrix}$

and for a parallel tuned pick-up is given by:

$\begin{matrix}{R_{AC} = {\frac{\pi^{2}}{8}R_{DC}}} & (3)\end{matrix}$

While nominally there is some reactance introduced by the rectifier dueto its non-linear characteristic for both series and parallel tunednetworks which would result in mistuning the resonant network, thisreactance is normally accounted for in the pick-up tuning capacitance.Hence it is not explicitly discussed here.

As the DC output is represented by its equivalent AC load, the reflectedimpedance of these three ideally tuned pick-up topologies can bedirectly applied here and are shown below:

$\begin{matrix}{Z_{r} = \{ \begin{matrix}{\frac{\omega^{2}M^{2}}{R_{AC}} = {\frac{\omega \; M^{2}}{L_{2}}Q_{2}}} & {{series}\mspace{14mu} {tuned}} \\{{\frac{M^{2}}{L_{2}^{2}}( {R_{AC} - {j\; \omega \; L_{2}}} )} = {\frac{\omega \; M^{2}}{L_{2}}( {Q_{2} - j} )}} & {{parallel}\mspace{14mu} {tuned}} \\{\frac{\omega^{2}M^{2}R_{AC}}{X_{2}^{2}} = {\frac{\omega \; M^{2}}{L_{2}}Q_{2}}} & {{LCL}\mspace{14mu} {tuned}}\end{matrix} } & (4)\end{matrix}$

X₂ is the characteristic impedance of a series-parallel LCL tunedpick-up.

Equation (4) illustrates that the reflected impedance of both the seriestuned and the LCL tuned pick-up have the same characteristic. Thereflected load is purely resistive and is directly proportional to thepick-up loaded Q₂ when the pick-up coil is tuned in situ. As these twotopologies share the same characteristic, in this document only theparallel-tuned and the series-tuned pick-ups are considered forvariations in magnetic coupling.

Load Modelling of a Mistuned Primary and Secondary Resonant Network

In order to investigate the reactive load seen by the primary powersupply due to a combination of both a mistuned primary and secondaryresonant network, the reflected impedance of both a mistunedseries-tuned and a mistuned parallel-tuned pick-up are considered. Amodel is developed, which, in conjunction with measured track tuningvariations, allows the reactive load in the power supply inverter bridgeto be calculated. In this section the load model of a mistuned pick-upis presented, followed by the model of a mistuned primary resonantnetwork.

Reflected Impedance of Mistuned Pick-Up

-   -   a) Series Tuned

The conceptual diagram of a mistuned series-tuned pick-up is shown inFIG. 4. The terms L₂₀ and C₂₀ are the (designed) nominal value of thepick-up inductance and its tuning capacitance. The variation in thepick-up inductance is modelled using the term ΔL₂ i.e. a given charge inreactance which is defined by:

ΔL ₂ =L ₂ −L ₂₀  (5)

where L₂ is the pick-up inductance at the current physical position. Theinput impedance of the series-tuned pick-up Z_(2s) is given by:

$\begin{matrix}\begin{matrix}{Z_{2s} = {R_{AC} + {j\; \omega \; L_{20}} + \frac{1}{j\; \omega \; C_{20}} + {j\; {\omega\Delta}\; L_{2}}}} \\{= {R_{AC} + {j\; {\omega\Delta}\; L_{2}}}}\end{matrix} & (6)\end{matrix}$

The definition of the pick-up reflected impedance Z_(r) presented isgiven by:

$\begin{matrix}{Z_{r} = \frac{\omega^{2}M^{2}}{Z_{2}}} & (7)\end{matrix}$

Substituting (6) into (7), the mistuned series-tuned pick-up reflectedimpedance Z_(rs) is then given by:

$\begin{matrix}{Z_{rs} = {\frac{\omega^{2}M^{2}R_{AC}}{R_{AC}^{2} + ( {{\omega\Delta}\; L_{2}} )^{2}} - {j\frac{\omega^{2}{M^{2}( {{\omega\Delta}\; L_{2}} )}}{R_{AC}^{2} + ( {{\omega\Delta}\; L_{2}} )^{2}}}}} & (8)\end{matrix}$

Unlike the parallel tuned pick-up, where there is a load independentreflected reactance (−jM²/L₂), which is discussed further below, thereflected impedance of a series tuned pick-up is load dependent asdemonstrated in (8). Therefore, for a series tuned pick-up the loaddependent reflected impedance ΔZ_(rs) is the same asZ_(rs)(ΔZ_(rs)=Z_(rs)). From (8), it can be seen that ΔL₂ causes areflected reactance, which has the opposite polarity to ΔL₂. The realand the imaginary parts of (8) share many common terms, and it isconvenient to derive an expression for the ratio between the reactiveand the real load:

$\begin{matrix}{\frac{{Im}( Z_{rs} )}{{Re}( Z_{rs} )} = {{- Q_{20}}\gamma}} & (9)\end{matrix}$

where γ is the per unit (pu) variation of ΔL₂ with respect to thedesigned tuning inductance L₂₀ and is defined by:

$\begin{matrix}{\gamma = {\frac{L_{2} - L_{20}}{L_{20}} = \frac{\Delta \; L_{2}}{L_{20}}}} & (10)\end{matrix}$

and Q₂₀ is the nominal loaded quality factor of the pick-up when tunedat the designed operating position, defined by:

$\begin{matrix}{Q_{20} = \frac{\omega \; L_{20}}{R_{AC}}} & (11)\end{matrix}$

In a battery charging application running at a constant output voltageand power for the majority of the time, the load R_(AC) and hence Q₂₀are normally maintained constant. Therefore, (9) is a very usefulexpression for estimating the reactive power as it only consists of thedesigned circuit Q₂₀ and the pick-up inductance variation and directlyindicates the polarity of the reflected reactive power.

Using the reflected resistive load in (8), the track current (I_(1s))required to deliver the desired output power can be simply calculatedusing P=Re(Z_(rs))I_(1s) ² and is given by:

$\begin{matrix}\begin{matrix}{I_{1\; s} = {\frac{1}{\omega \; M}\sqrt{\frac{P_{out}( {R_{AC}^{2} + ( {{\omega\Delta}\; L_{2}} )^{2}} )}{R_{AC}}}}} \\{= {\frac{1}{\omega \; M}\sqrt{P_{out}{R_{AC}( {1 + ( {Q_{20}\gamma} )^{2}} )}}}}\end{matrix} & (12)\end{matrix}$

Using (12), the increase in track current I₁ as a result of the pick-upbeing mistuned can be expressed by:

$\begin{matrix}{\frac{I_{1\; s_{—}{mistuned}}}{I_{1\; s_{—}{tuned}}} = \sqrt{1 + ( {Q_{20}\gamma} )^{2}}} & (13)\end{matrix}$

b) Parallel Tuned

The conceptual diagram of a mistuned parallel-tuned pick-up is shown inFIG. 5. Here the variation in tuning due to variations in L₂ isrepresented using the term ΔC₂ which is given by:

$\begin{matrix}{{\Delta \; C_{2}} = {{\frac{1}{\omega^{2}}( {\frac{1}{L_{20}} - \frac{1}{L_{2}}} )} = {C_{20} - C_{2}}}} & (14)\end{matrix}$

where C₂₀ is the nominal tuning capacitance with the designed value ofL₂₀, and C₂ is the ideal tuning capacitance value of L₂. Using a Nortontransformation on the pick-up resonant network, the pick-up coilcurrent, and hence the pick-up reflected impedance Z_(rp), can bedescribed by:

$\begin{matrix}{Z_{rp} = {\frac{M^{2}\text{/}R_{AC}}{\frac{L_{2}^{2}}{R_{AC}^{2}} + {L_{2}^{2}( {{\omega\Delta}\; C_{2}} )}^{2}} - {j\frac{\omega \; M^{2}}{L_{2}}} - {j\frac{\omega \; M^{2}\Delta \; C_{2}}{\frac{L_{2}^{2}}{R_{AC}^{2}} + {L_{2}^{2}( {{\omega\Delta}\; C_{2}} )}^{2}}}}} & (15)\end{matrix}$

This expression (15) indicates that the reflected impedance of amistuned parallel-tuned pick-up, has two reactive components. The firstone is the reactive (capacitive) component (−jωM²/L₂) which wasdescribed in (4). This capacitive component is independent of the loadbut proportional to the magnetic coupling. It is normally included inthe primary track inductance when the power supply operates with aparallel-tuned pick-up at setup for systems with constant coupling (suchas monorail systems). Variations in this term (−jωM²/L₂) due to changesin the magnetic structure will not be discussed here as this is regardedas a change in the primary track inductance due to physical movement ofthe charging pad, but will be discussed further below. Therefore, theload dependent variable reflected reactive load is then defined as:

$\begin{matrix}{{\Delta \; Z_{rp}} = {Z_{rp} - ( {{- j}\frac{\omega \; M^{2}}{L_{2}}} )}} & (15)\end{matrix}$

Similar to the series-tuned pick-up, the second reactive component isintroduced by the variable capacitor ΔC₂ and exhibits a polarityopposite to that of ΔC₂. The ratio between the load dependent variablereflected reactive load, which excludes the (−jωM²/L₂) term, and theresistive load is given in (16) and it is nearly identical to (9) forthe series-tuned pick-up.

$\begin{matrix}{\frac{{Im}( {\Delta \; Z_{rp}} )}{{Re}( Z_{rp} )} = {{- Q_{20}}\delta}} & (16)\end{matrix}$

Here δ is the variation of ΔC₂ with respect to the designed tuningcapacitance C₂₀ and is defined by:

$\begin{matrix}{\delta = {\frac{\Delta \; C_{2}}{C_{20}} = {\omega^{2}L_{20}\Delta \; C_{2}}}} & (17)\end{matrix}$

The nominal loaded quality factor Q₂₀ of the pick-up when tuned at thedesigned operating position is defined by:

$\begin{matrix}{Q_{20} = \frac{R_{AC}}{\omega \; L_{20}}} & (18)\end{matrix}$

Using the resistive term of (15), the required track current for amistuned parallel-tuned pick-up is then:

$\begin{matrix}\begin{matrix}{I_{1\; p} = {\frac{L_{2}}{M}\sqrt{{PR}_{AC}( {\frac{1}{R_{AC}^{2}} + ( {{\omega\Delta}\; C_{2}} )^{2}} )}}} \\{= {\frac{L_{2}}{M}\sqrt{\frac{P}{R_{AC}}( {1 + ( {Q_{20}\delta} )^{2}} )}}}\end{matrix} & (19)\end{matrix}$

Using (19), the increase in track current I₁ due to the pick-up beingmistuned is given in (20), and as expected, is similar to (13):

$\begin{matrix}{\frac{I_{1\; p_{—}{mistuned}}}{I_{1\; p_{—}{tuned}}} = \sqrt{1 + ( {Q_{20}\delta} )^{2}}} & (20)\end{matrix}$

Load Modelling of the Primary Resonant Network

The conceptual diagram of a voltage-sourced LCL resonant power supply isshown in FIG. 6 with the pick-up equivalent reflected impedance(Re(Z_(r))+jIm(ΔZ_(r))). As the reflected reactance is in series withthe primary track inductance L₁, it is convenient to interpretIm(ΔZ_(r)) in terms of inductance. To define this pick-up equivalentreflected inductance L_(r), the operating frequency ω is considered:

L_(r)=Im(ΔZ_(r))/ω(21) The measured primary track inductance L₁ withinthe given pick-up movement tolerance is separated into two componentshere: L₁₀ and a given change in reactance ΔL₁ (L₁=L₁₀+ΔL₁). L₁₀ is thenominally designed track tuning inductance, and its reactance combinedwith C_(L1) is the primary LCL network characteristic impedance X. ΔL₁represents the difference between the measured track inductance L₁ andthe nominal track inductance L₁₀. However, the total inductancevariation seen by the power supply ΔL_(l) is a combination of ΔL₁ andthe pick-up reflected inductance L_(r) as illustrated in FIG. 6 and(22). Thus it is difficult to estimate the overall inductance variationΔL_(l) while choosing the tuning value L₁₀ based on measured L₁.

$\begin{matrix}\begin{matrix}{{\Delta \; L_{l}} = {L_{1} - L_{10} + \frac{{Im}( {\Delta \; Z_{r}} )}{\omega}}} \\{= {{\Delta \; L_{l}} + L_{r}}} \\{= {\Delta \; X_{l}\text{/}\omega}}\end{matrix} & (22)\end{matrix}$

Here ΔX_(l) is the total output reactive load of the LCL network.

Instead of choosing the tuning value L₁₀ based only on the measuredvalue L₁, we have found that a preferable approach is to firstly combinethe calculated pick-up reflected inductance L_(r) together with L₁ toform one single inductive component called L_(1eqv), which is the totalequivalent track inductance seen by the tuning capacitor C_(L1) asillustrated in Figure and in (23).

$\begin{matrix}\begin{matrix}{L_{1\; {eqv}} = {L_{1} + L_{r}}} \\{= {L_{10} + {\Delta \; L_{l}}}}\end{matrix} & (23)\end{matrix}$

Then based on the value of L_(1eqv), L₁₀ can now be designed to minimisethe variation in the total track inductance and to achieve a desirablepattern of ΔL_(l), within the misalignment tolerance, in order tominimise the reactive load within the primary power supply. Thisminimisation process is explained further below. The LCL network outputimpedance Z_(l) is expressed by:

$\begin{matrix}\begin{matrix}{Z_{l} = {{{Re}( Z_{r} )} + {j\; {\omega ( {{\Delta \; L_{l}} + L_{r}} )}}}} \\{= {{{Re}( Z_{r} )} + {j\; \Delta \; X_{l}}}}\end{matrix} & (24)\end{matrix}$

Using (24), the input impedance (Z_(in)) of the primary LCL network isgiven by:

$\begin{matrix}\begin{matrix}{Z_{in} = \frac{X^{2}}{Z_{l}}} \\{= \frac{X^{2}}{{{Re}( Z_{r} )} + {j\; \Delta \; X_{l}}}} \\{= {\frac{X^{2}{{Re}( Z_{r} )}}{{{Re}( Z_{r} )}^{2} + {\Delta \; X_{l}^{2}}} - {j\frac{X^{2}\Delta \; X_{l}}{{{Re}( Z_{r} )}^{2} + {\Delta \; X_{l}^{2}}}}}}\end{matrix} & (25)\end{matrix}$

The input displacement power factor (DPF_(LCL)) of the primary LCLresonant network is then given by:

$\begin{matrix}\begin{matrix}{{DPF}_{LCL} = \frac{{Re}( Z_{in} )}{\sqrt{{{Re}( Z_{in} )}^{2} + {{Im}( Z_{in} )}^{2}}}} \\{= \frac{{Re}( Z_{r} )}{\sqrt{{{Re}( Z_{r} )}^{2} + {\Delta \; X_{l}^{2}}}}}\end{matrix} & (26)\end{matrix}$

Using the V_(B) _(—) ₁ expression in (1) and (26), for a given powerP_(out) the fundamental component of the inverter bridge current I_(B)_(—) ₁ is then given by:

$\begin{matrix}\begin{matrix}{I_{B_{—}1} = \frac{P_{out}}{{DPF}_{LCL}V_{B_{—}1}}} \\{= \frac{P_{out}}{{DPF}_{LCL}I_{1}X}}\end{matrix} & (27)\end{matrix}$

Design Considerations

a) Additional Pick-Up Reactive Power Due to Mistuning

The additional reactive load Im(ΔZ_(r)) of both the series-tuned andparallel-tuned pick-ups, reflected back onto the track is proportionalto the loaded Q₂₀ and the tuning variation γ or δ respectively.Im(ΔZ_(r)) also represents an increase in the reactive load within thepick-up resonant network compared with an ideally tuned pick-up.Practical measurements of charging pad inductance indicate that the padinductance has a variation of typically 2-7% depending on allowed(expected) misalignment. The pick-up loaded Q₂ for conventionaldistributed IPT systems is typically designed to be below 10 and for apractical IPT battery charging system is normally kept below 6. With aQ₂₀ value of 6, the additional reactive load is between 12-42% of thereal power. If the magnetic structure has a bigger inductance variation(δ or γ>0.15), for the same Q₂₀ of 6, the additional reactive load wouldbe 90% of the real power. This increases the stress in the pick-upresonant components and thus the component ratings need to besignificantly higher than would be indicated by an ideally tuned design.

b) Increase of Track (Primary Pad or Winding) Current with MistunedPick-Up

Both (13) and (20) illustrate that the track current needs to beincreased to deliver the same output power (constant Q₂₀ and R_(AC) forprimary side current control) to a mistuned pick-up. However, increasingI₁ also increases the track conduction loss. The square of the requiredtrack current increase (I_(t) _(—) _(mistuned)/I₁ _(—) _(tuned))², whichrepresents the increase in the conduction loss, as a function of thepick-up tuning variation γ and δ with various values of Q₂₀ is shown inFIG. 7. With a Q₂₀ of 3 and with a pick-up tuning variation of 7.5%, theincreased conduction loss is 5% compared with a pick-up that is alwaystuned. With the same tuning variation but a Q₂₀ of 6, the conductionloss increase is 4 times higher (20%) as shown in FIG. 7.

As illustrated in (12) and (19), the required track current to achievethe same Q₂₀ is inversely proportional to the coupling condition. Thus,the increase in the track conduction loss will be more significant atoperating positions with low coupling compared to operating positionswith higher coupling. If a design decision is made to minimise thecharging pad conduction loss without using self-tuning circuitry on thesecondary side, the best practice for systems with high Q₂₀ (near 6) andhigh inductance variation (γ or δ>0.1) is to ensure the pick-up is tunedat the operating position with the lowest coupling.

c) Reactive Power Flow of the LCL Network

The input DPF of the primary LCL network is controlled by its outputreactive load ΔX_(l) as illustrated in (26) where Re(Z_(r)) is assumedto be constant at a fixed operating position during steady state.Therefore, choosing the primary tuning ωL₁₀, which determines ΔX_(l), iskey to determining the burden of reactive load on the inverter bridgewithin the specified pad power transfer zone. There are twoconsiderations when choosing the primary tuning ωL₁₀ and they arediscussed following in this section.

(i) Ensuring Inductive Load (Z_(in)) for Inverter Bridge Voltage V_(B)_(—) ₁

The LCL tuning network has an impedance converting characteristic asillustrated in (25). Therefore by ensuring ΔX_(l) is either zero orcapacitive within the misalignment tolerance, Z_(in) is ensured to beeither pure resistive or only slightly inductive. Thus, the DPF betweenV_(B) _(—) ₁ and I_(B) _(—) ₁ is either unity or slightly lagging whichis normally preferred in inverter bridge design to prevent undesirableswitching losses due to the diode reverse recovery currents in theswitches.

(ii) Reactive Power Minimisation of the Primary LCL Network

In order to minimise the reactive load and to achieve the best possibleinput DPF of the primary LCL network, both the pick-up tuning ωL₂₀ andthe primary tuning ωL₁₀ need to be chosen carefully to result in adesirable variation pattern of ΔX_(l). Using the expressions for therequired track current in series and parallel-tuned pick-ups given in(12) and (19) respectively, the common definition of the LCL networkoutput reactive power can be expressed by:

$\begin{matrix}\begin{matrix}{{VAR} = {I_{1}^{2}\Delta \; X_{l}}} \\{{\propto \frac{\Delta \; X_{l}}{M^{2}}}}\end{matrix} & (28)\end{matrix}$

This indicates that the additional reactive load within the LCL networkis proportional to ΔX_(l) and inversely proportional to M² whichrepresents the relative coupling variation for a given charging paddesign. Therefore, in order to minimise the reactive load, the variationin ΔX_(l) should be minimised at an operating position where thecoupling (M²) is at its lowest, so that the overall reactive load seenby the inverter bridge is minimised.

d) Inverter Bridge Current

Using the track current expressions in (12) and (19), and the inverterbridge current I_(B) _(—) ₁ expression in (27), I_(B) _(—) ₁ can now beexpressed in terms of the output power, the mutual coupling and the DPF,as shown in (29), indicating that I_(B) _(—) ₁ is directly proportionalto the output power and the magnetic coupling.

$\begin{matrix}{I_{B_{—}1} \propto \frac{P_{out}M}{{DPF}_{LCL}}} & (29)\end{matrix}$

For a variable coupling system using primary side current control, theinverter bridge current will necessarily have the same range ofvariation as the magnetic coupling in order to maintain the output powerto be constant. This bridge current variation needs to be treatedcarefully and the power supply inverter design necessarily needs to berated for the maximum possible coupling variation.

-   -   e) Design Flow Chart

As discussed earlier, conventionally, the tuning network of a lumpedcoil system is designed based on the physically measured charging padinductances at the same operating position, which then becomes theoptimum position of operation. However, when designing tuning networksfor lumped coil systems with a specified power transfer zone, there area number of design issues that need to be considered in order to achievea suitable result.

In practice, it is difficult to achieve all the considerations presentedabove in one tuning network. To assist the design process, a design flowchart which combines the considerations discussed earlier is presentedin FIG. 8. This flow chart presents a sequence of design steps, forselecting one or more components of the primary and/or secondaryresonant network to achieve one or more practical outcome, such ascontaining the reactive load seen by the primary power supply. Referringto FIG. 8, the process begins at 101 and the “default” objective is tominimise pad conduction loss at 102. The first design step 103 is toselect L₂₀ to design the secondary tuning at the operating position withthe lowest coupling. Then in step 104 ωL_(1eqv) is calculated, havingdesigned the pick-up (i.e. secondary) tuning, L_(R) is known andL_(1eqv) can be calculated from the initial measured value of L₁. Nextin step 105 ΔωL₁₀ is chosen so that ΔX₁ is only zero or capacitive.Choosing ΔX₁ to be capacitive means that means that it is seen as aninductive load by the power supply i.e. the H bridge of the converterwhich energises the primary network. In step 106 the reactive load canbe further considered in order to ensure that the input displacementpower factor for the primary LCL network is improved by proceedingthrough a loop to step 107 to check whether all the L₂₀ and L₁₀ tuningcombinations have been covered. If they haven't, then the ΔX₁ variationis stored in step 108 and in step 109 the L₂₀ value is changed to allits measured highest coupling operating position and the process returnsto step 104 wherein ωL_(1eqv) is calculated again. If at step 106 noimprovement is required to the input displacement power factor, then atstep 110 the primary LCL network input current is calculated togetherwith the displacement power factor variation and the flow chart ends atstep 112. If at step 107 all L₂₀ and L₁₀ tuning combinations have beenconsidered, then the process proceeds to step 111 at which the L₂₀ andL₁₀ combination value which gives the lowest variation in reactive loadi.e. lowest ΔX₁ at the lowest coupling position as chosen followingwhich the process returns to step 110. It will be appreciated that thisis simply one methodology which can used to enable the invention. Adesign example is now considering the primary tuning L₁₀ in order toachieve the design requirements which include minimising the primary padconduction loss, or achieving the best possible input DPF in the primaryLCL network. The default design focus is to minimise the primarycharging pad conduction loss and thus the pick-up tuning is designedaccordingly. If minimising the reactive load in the primary resonantnetwork is the priority, the primary and the secondary tuning is thenadjusted to achieve this.

Further examples are shown in FIGS. 8 a to 8 c. In FIG. 8 a the designobjective is to minimise the reactive loading on the inverter bridgei.e. minimise the reactive loading seen by the power supply. The processstarts in step 114, then L₂₀ is selected in step 115. ωL_(1eqv) iscalculated in step 116 following which ωL₁₀ is chosen at step 117. Thedisplacement power factor and primary current variation are calculatedin step 118 and results stored in step 119. At step 120 a decision ismade as to whether L₂₀ has become the maximum or minimum value of L₂within the charging zone which determines a given variation in coupling.If yes, then the process ends with selecting the values of L₁₀ and L₂₀which give the best power factor variation. If no, then the value of L₂₀is increased and the process returns to step 116.

In FIG. 8 b the design objective is to minimise the primary current i.e.minimise primary pad conduction loss. The process starts at step 124following which L₂₀ is selected at the point of lowest coupling in thespecified area of coupling variation determined by the required chargingzone. ωL_(1eqv) is calculated in step 126 following which ωL₁₀ is chosenat step 127. The displacement power factor and primary current variationare calculated in step 128 to complete the process.

In FIG. 8 c the design objective is to minimise additional pick-up(secondary) reactive power due to mistuning. The process starts at step130. The primary winding current control topology is then selected instep 131. If primary side control is used, then the process proceeds tostep 132 in which L₂₀ is chosen to be in the middle of the L₂ variationwithin the charging zone. Then ωL_(1eqv) is calculated at step 133 andωL₁₀ is chosen in step 134. The process ends at step 142 in which thedisplacement power factor and primary current variation are calculated.If instead a constant track current topology is used, then the processproceeds from step 131 to 135 in which L₂₀ is selected for the operatingposition with lowest coupling. Then ωL_(1eqv) is calculated at step 136and ωL₁₀ is chosen in step 137 before the final step 142. If instead acombination of primary side and secondary side control topology is used,then the process proceeds from step 131 to 138 in which the Q₂ profileis calculated assuming a perfectly tuned pick-up then L₂₀ is selectedfor tuning at the position of maximum Q₂₀. Then ωL_(1eqv) is calculatedat step 140 and ωL₁₀ is chosen in step 141 before the final step 142.

Design Example

A tuning network for a 1.2 kW EV battery charging system designed usingthe strategy described with reference to FIG. 8 is now presented by wayof example. The analytical results determined using the designed networkare compared against systems with charging pad tuning networks designedat both the maximum and minimum coupling position to demonstrate theimprovement in the input loading variation of the primary LCL network.The analytical results of the proposed design are also verified againstSPICE simulations.

System Parameters

a) Primary Power Supply

The conceptual structure of the 1.2 kW battery charging system is shownin FIG. 9 and its parameters are given in Table 1 below. The inverterbridge voltage V_(B) _(—) ₁ has a voltage variation range of 0 to 225VRMS to perform primary side current control for regulating the powerflow to the pick-up load (R_(AC)). As explained in Section 0, the ACload R_(AC) has different values for series and parallel-tuned pick-upsin order to have the same equivalent DC output power and voltage.

TABLE 1 Parameters of the 1.2 kW battery charging system V_(B) _(—) ₁range 0-225 V L_(B)   87 μH P_(out)  1.23 kW RMS Frequency 20 kHz C_(B)1.043 μF R_(AC) (series) 26.34 Ω TX turns 1:2 C₁ 0.602 μF R_(AC)(parallel)   40 Ω ratio X_(LCL) 13.22 Ω I₁ max 34 A RMS

b) Charging Pad Magnetic Structure

The selected charging pad magnetic structure in this design example is a700 mm circular charging pad. The operating air gap is between 100 mmand 150 mm with a lateral tolerance of ±100 mm. This forms a rectangularboundary within a specified power transfer zone as illustrated in FIG.10. The position where the pick-up pad is at the tightest couplingposition (closest to the primary pad) is labelled “A” and the positionwhere the pick-up pad has the lowest coupling position is labelled “B”in the diagram. The proposed tuning strategy and conventional tuningmethods are examined with the pick-up pad moving along the horizontalboundary (δx from 0 to 100 mm) at the extreme vertical boundary (150 mmand 100 mm).

The magnetic structures of both charging pads are identical. The primarypad adopts a bi-filar winding with 12 turns. Regarding the secondarypad, a different number of turns is used for the series andparallel-tuned pick-up. The series-tuned pick-up acts as a voltagesource and therefore boosts the current while the parallel-tuned pick-upacts as a current source and boosts its output voltage. In order forthese two tuning topologies to have the same output DC voltage and powerwith the same magnetic structure, the number of turns on the pick-up padneeds to be designed for a suitable open circuit voltage (V_(oc)) andshort circuit current (I_(sc)) ratio. The winding structure of each ofthe charging pads which achieves the same equivalent DC outputcharacteristics used in this design example is outlined in Table 2.

TABLE 2 Winding structures of the 700 mm circular charging pad for bothprimary and secondary Winding structure Primary charging pad Bi-filarwith 12 turns (2 × 12 turn) Secondary charging pad: Single wire with 24turns series-tuned pick-up Secondary charging pad: Bi-filar with 12turns (2 × 12 turn, parallel-tuned pick-up identical to the primary pad)

Measured inductances of the circular charging pad at an air gap of 100mm and 150 mm with x direction movement between 0 to 100 mm are shown inFIG. 11. The open-circuit bi-filar pad inductance measurements are forprimary pad tuning when a series-tuned pick-up is used, while theshort-circuited inductance measurements are for primary pad tuning whena parallel-tuned pick-up is used. This is because the short-circuitedmeasurements include the pad self-inductance L₁ and pick-up reflectedcapacitive component (−M²/L₂) as illustrated in (30).

$\begin{matrix}{L_{1\; {sc}} = {L_{1} - \frac{M^{2}}{L_{2}}}} & (30)\end{matrix}$

Since the secondary charging pad in a parallel-tuned pick-up has thesame winding structure as the primary pad, the self-inductance of thesecondary pad is identical to the measured primary self-inductance shownin FIGS. 11 (a) and (b). The measured secondary pad self-inductance witha single wire wound structure as used in the series-tuned topology isshown in FIGS. 11 (c) and (d). The calculated mutual inductance usingthe open-circuit and short-circuit measurements are shown in FIGS. 11(e) and (f). This calculated mutual inductance is referred back to theprimary side. When using this calculated mutual inductance value with aseries-tuned pick-up, a turns ratio of 2 needs to be taken into account.

These measurements indicate that the charging pad self-inductance has avariation of 7% from the operating position with maximum coupling(labelled A on the graph) to the minimum coupling position (labelled Bon the graph). This variation occurs due to the relative physicalmovement between the ferrimagnetic materials and the coils in thecharging pad. The coupling variation between the two extreme points Aand B is about a factor of two as shown in Figure (e) and (f) where themutual inductance varies from 55 μH to 23 μH. Performances of thevarious tuning options.

Performances of the Various Tuning Options

In this design example, the maximum variation in inductance is below 7%and the value of the loaded Q₂ is below 3, which is given in the nextsection. With such low inductance variations and a small Q₂, therequired increase in track current to deliver the rated power with amistuned pick-up is only in the range of 2-3% as illustrated in FIG. 7.Therefore, the pick-up is not necessarily required to be tuned at theminimum coupling position B, so the tuning network design focus is thento minimise the input load variation of the primary LCL network. Theperformance of the system, designed using the proposed strategy, iscompared against systems with both charging pads designed at the maximumcoupling position, which is referred to as “AA”, and at the minimumcoupling position, which is referred to as “BB”.

a) Series Tuned Pick-Up

The parameters of the tuning network designed at operating position AA,BB and designed using the proposed methodology discussed in connectionwith FIG. 8 are given in Table 3 below. In the design using the proposedmethodology, the nominal tuning value of the pick-up pad L₂₀ is itsself-inductance at the minimum coupling position B and the nominaltuning value of the primary pad is a calculated value of 128 μH asdetermined from FIG. 12 (d) and explained later. The analytical resultsof these three tuning network designs are shown in FIG. 12 and theproposed design is verified with SPICE simulations which are shown inFIG. 13.

TABLE 3 Tuning network parameters of the various tuning options forseries-tuned pick-up AA: L₁₀:  134.8 μH C_(L1):  2.14 μF L₂₀: 571.31 μHQ₂₀: 2.73 Max. γ: −0.0607   BB: L₁₀: 126.57 μH C_(L1): 2.963 μF L₂₀:536.61 μH Q₂₀: 2.56 Max. γ: 0.0647 New tuning L₁₀:   128 μH C_(L1):2.778 μF L₂₀: 536.61 μH design: Q₂₀: 2.56 Max. γ: 0.0647

In the calculated pick-up reflected equivalent inductance L_(r) shown inFIGS. 12 (a) and (b), tuning option AA has the smallest variationcompared with tuning option BB and the new tuning design option. But inthe L_(1eqv) graph shown in FIGS. 12 (c) and (d), tuning option AA hasthe biggest primary inductance variation seen by the tuning capacitorC_(L1) compared with the other options. Since the biggest ΔX_(l) fortuning option AA occurs at the minimum coupling position, it has thebiggest reactive load variation at the input of the primary LCL networkas shown in FIG. 12 (e) to (h).

FIG. 12 (d) demonstrates that the biggest value of L_(1eqv) in the newtuning design is 128 μH and hence that is the chosen L₁₀ value. Althoughoption BB demonstrates the best DPF performance compared with the newtuning as shown in FIG. 12( f), option BB also results in a capacitiveload at the input of the LCL network for the pick-up pad moving in the xdirection at the 150 mm air gap. Therefore, the new tuning design hasminimised the primary DPF variation while keeping the load on theinverter bridge inductive. The SPICE simulation results of the newtuning design, given in FIG. 13, show very good agreement with theanalytical results.

b) Parallel Tuned Pick-Up

The parameters of the tuning network designed at operating position AA,BB and the new tuning design are given in Table 4. In the new tuningdesign the nominal tuning value of the pick-up pad L₂₀ is itsself-inductance at the maximum coupling position A and the nominaltuning value of the primary pad is calculated to be 123.8 μH asdetermined from FIG. 14 (d) and explained later. The analytical resultsof these three tuning network designs are shown in FIG. 13 and theproposed design is verified against SPICE simulations shown in FIG. 15.

TABLE 4 Tuning network parameters of the various tuning options forparallel-tuned pick-up AA: L₁₀: 111.81 μH C_(L1): 9.58 μF L₂₀: 134.8 μHQ₂₀: 2.36 Max. δ: −0.065 BB: L₁₀: 122.17 μH C_(L1): 3.73 μF L₂₀: 126.57μH  Q₂₀:  2.515 Max. δ:   0.061 New tuning L₁₀:  123.8 μH C_(L1):  3.4μF L₂₀: 134.8 μH design: Q₂₀: 2.36 Max. δ: −0.065

In the calculated pick-up reflected equivalent inductance (L_(r)) andthe primary L_(1eqv) inductance shown in FIG. 14 a)-(b) and (c)-(d)respectively, tuning option AA and the new tuning design have thesmallest variation compared with tuning option BB. In the L_(1eqv) graphshown in FIG. 14 (d), the calculated L_(1eqv), graph has a maximum valueof 123.8 μH and hence that is the chosen L₁₀ value for the design.

Although tuning option AA has the same L_(1eqv) variation as the newtuning design, FIG. 14 (e) to (f) indicate that option AA has the biggerreactive load variation and is capacitive. The reason for this is thatthe primary is tuned at position A so the biggest variation of ΔX_(l)occurs at the minimum coupling position B which then results in thebiggest additional reactive load compared with others. The analyticalresults in FIG. 14 (e) to (f) also demonstrate that the new tuningdesign is inductive and has the least input DPF variation, which isbetween unity and 0.976. The SPICE simulation results of the new tuningdesign are shown in FIG. 15 and again demonstrate very good agreementwith the analytical results.

Inverter Bridge Current Variation

As discussed in above, the inverter bridge current is directlyproportional to the coupling of the magnetic structure. In this designexample, the mutual inductance of the charging pad varies from 23 μH to55 μH. This implies that the inverter bridge current will also have samedegree of variation.

The SPICE simulation results for the inverter bridge voltage and currentoperating under the rated load of 1.2 kW with both series andparallel-tuned pick-ups are shown in FIG. 16 (a) to (d). The tuningnetworks are designed using the proposed strategy of Section 0 so thereactive component in the bridge current has been minimised as much aspossible. The simulation results show that the inverter bridge voltagevaries from 90 to 200V RMS as the coupling changes while the inverterbridge current varies from 15 to 6 A RMS. In order to lower the LCLnetwork input voltage from 200V RMS to 90V RMS, the inverter bridge willnecessarily be working over a wide variation of phase shifts θ toachieve a wide V_(B) _(—) ₁ variation. While the inverter bridgeoperates with small phase shifts to lower V_(B) _(—) ₁, the currentI_(B) _(—) ₁ will be at its highest value, as illustrated in FIG. 16.For higher power systems, in the range of 7 kW, this wide variation ofI_(B) _(—) ₁ complicates the inverter bridge design and makes thesemi-conductor switch selection difficult.

Alternative Magnetic Structure

The developed tuning network design strategy can be used on any magneticstructure. The key parameter, as mentioned in the circular pad example,is the boundary of movement or tolerance within the specified powertransfer zone. The circular pad has rotational symmetry therefore thedesign example requires only lateral direction of movement with verticalmovement to determine the tuning design. For a Double D (referred toearlier in this document) charging pad, the defined boundary of thepower transfer zone is a rectangular prism as illustrated in FIG. 17.This is due to its polarised structure. Therefore, in order to designthe tuning network for systems using Double D pads, the requiredinductance measurements are along the boundary of the two square plansat the extremes of vertical offset. These two plans are A-B-C-D andE-F-G-H as indicated in FIG. 17. Thus it will be seen that the inventionis applicable to wireless power transfer system which may use a varietyof magnetic structures.

Frequency Considerations

The standard approach has as described earlier has simply been to tunethe primary and secondary pads at a known fixed separation from eachother. Normally this is either at the closest and most centrally locatedposition A or at the furthest position B (as shown in FIG. 10). Giventhe primary and secondary pads are normally both tuned at one of theselocations, these two design options are labelled AA and BB in FIGS. 18to 26. For the examples described earlier then the shift in the actualtuned frequency of both the primary and secondary from the ideal systemoperational tuned frequency ωo due to allowable relative movement of thepads, can be viewed in FIGS. 10 and 11 for series tuned secondary or inFIGS. 23 and 24 for a system with a parallel tuned secondary. Here thevariations in tuned frequency arise only due to the relative movement ofthe pads, but other factors such as mistuning over time can add to thechange. As shown, this can cause large changes in the natural resonanttuned frequency (ω₁) of the primary pad during operation or of thenatural resonant frequency (ω₂) of the secondary pad during operation. Asmaller variation (spread) in the tuned frequency of either ω₁ or ω₂ isnaturally beneficial, and if this variation controlled so that it iswhatever is best for the power supply (e.g. in an LCL primary network itis best to be capacitive, which translates to an inductive load viewedfrom the power supply) so that the inverter only needs to produce extrainductive VARs (due to this mistuning) during operation, then that isalso beneficial.

In FIG. 18 the primary and secondary pads are tuned at the AA positionand the secondary resonant network is series tuned. Referring to thatFigure, arrow 201 shows the operating frequency of the primary atposition A, which has the system operating frequency ω₀ of 20 kHz. Asthe secondary is moved from position A to position B sat 202, thefrequency of the primary moves from 20 khz to 20.83 khz. This change isrepresented by Δω₁ and is based on measuring the inductance changesbetween the two positions when the system is not operational. However,as we have described earlier, the variation in frequency of the primarybased on those inductance measurements is actually incorrect. Instead,the actual resonant frequency variation during operation is representedby arrow 203. This shows that the initial resonant frequency at positionA which is 20 kHz as represented by arrow 201, changes to 20.66 kHz whenthe secondary is moved to position B, as indicated by arrow 203.

Similarly, the change in the resonant frequency of the secondary networkduring operation is illustrated by arrows 204 and 205. Arrow 204represents the secondary at position A operating at 20 kHz (in theposition at which it was tuned) and the frequency at position B isindicated by arrow 205 being 20.64 kHz. The change in frequency of thesecondary is represented by Δω₂.

Referring to FIG. 19, the performance of a system tuned at the BBposition with a series tuned pick-up is shown. Arrow 206 shows theexpected operating frequency of the primary at position A based oninductance measurements when the system is non-operational. Arrow 207shows the operating frequency of the primary at position B which is 20kHz as expected. The actual variation in frequency is quite differentand is explained by the fact that both the reactance of the primary andsecondary networks are changing and the coupling between the networks ischanging, as described above. As can be seen, arrow 208 represents theactual natural resonant frequency of the primary during operation atposition A. As the secondary is moved to position B, the frequencydecreases to a minimum of 19.87 kHz shown by broken line 209, and risesagain to the tuned frequency of 20 kHz when the secondary is moved toposition B. The natural resonant frequency of the secondary duringoperation at position A is shown by arrow 201, moving to the tunedfrequency at position B as shown by arrow 211.

Considering the series tuned secondary example of FIGS. 18 and 19, thissystem tuned at AA has a much larger variation in ω₁ compared with thesystem BB. The secondary tuning variations are similar but shiftedeither positive or negative. If the tuning is changed to that of FIG.20, where the secondary is tuned at position B and the primary atposition A then the variation in ω₁ can be kept small, but now it isshifted further away from the operating frequency, which is alsoundesirable. In FIG. 20, the expected frequencies for the primary basedon inductance measurements are shown by arrows 212 and 213 for positionsA and B respectively. The actual natural resonant frequencies duringoperation are shown by arrows 214 and 215. Again, the frequencydecreases to a minimum of 20.69 kHz at a location between points A andB. The actual frequency shift for the secondary is shown by arrows 215and 216 relating to positions A and B respectively.

Using the new design approach described within this specification, theresulting tuning frequency shifts can be both minimized and positionedclose to, but just above, wo as desired to ensure the supply sees aresistive inductive load for the power supply described earlier. This isshown in FIG. 21 in which the frequencies for the primary determinedfrom inductance measurement are show by arrows 217 and 218, and thosefor the actual natural resonant frequencies during operation are shownby arrows 219 and 220. The frequency variation for the secondary isshown by arrows 221 and 222. In this design the natural resonantoperating frequencies have been selected to constrain the variation inreactive load and thus constrain the variation in frequency for thegiven change in reactance (brought about by the changes in relativeposition of the primary and secondary).

FIGS. 22, 23 and 24 show the variations in tuned frequency of both theprimary and secondary operation under the design options of AA, BB andthe desired approach explained here when a parallel tuned secondary padis used. Again there are significant shifts in ω₁ in both FIGS. 22 and23, whereas FIG. 24 under the new design approach shows that thefrequency shift can be contained and kept inductive for the supply. Thearrows representing the frequencies at position A and 13 have the samereference numerals as those for the series tuned situation describedwith reference to FIGS. 18, 19 and 21.

If the pick-up resonant network is designed only to minimize its VA₂,then the design approach is slightly different as discussed below.

The design, shown in FIG. 25 (referring to the design approachesdiscussed earlier in the specification), determines the extent of thevariation of ω₂ and optimizes the tuning of the secondary so that ω₀ isapproximately in the centre of Δω₂ in order to minimize VA₂. Thus, asshown in FIG. 25, the frequency of the secondary at position A is shownby arrow 230, and at position B by arrow 231. After fixing the secondarytuning, the primary tuning is adjusted to minimize the spread of Δω₁around ω₀, In this process the variation between ω₁ and ω₂ (Δω₁₂) isalso constrained in order to minimise VA₁, thereby ensuring the primaryresonant network input PF variation is minimized and maintained as closeto unity as possible. Δω₁₂ indicates the amount of additional reactivepower required due to mistuning. Thus in this design the invention hasbeen used to select the frequencies so that the variation or sweep isitself constrained to be near to, or spread about, the operatingfrequency of the system i.e. ω₀, and the difference between the primaryand secondary natural resonant frequencies during operation has alsobeen constrained.

If a secondary resonant network is tuned in such a way so that itassists in the minimization of VA₁, without thought for VA₂ then thedesign shown in FIG. 26 results. Case 1 and case 3 in FIGS. 25 and 26show results expected from measured inductance rather than the resonantfrequency during operation which is shown in cases 2 and 4.

Here Δω₂ and Δω₁ are placed around ω₀ while also minimizing the overallΔω₁₂ variation at all possible physical positions of the magneticsapparatus in order to minimise VA₁. Consequently the primary resonantnetwork input PF variation is minimized while maintaining it as close tounity as possible. The Secondary tuning variation is no longer centered(or nearly centered) around ω₀.

1. A wireless power transfer primary resonant network including: aprimary winding capable of being energised to provide a magnetic field;and at least one reactive tuning component selected to constrain thereactive loading on a power supply which energises the primary resonantnetwork, the reactive tuning component being selected dependent on agiven variation in inductance or capacitance of the primary resonantnetwork and a given variation in inductance or capacitance of asecondary resonant network coupled to the primary resonant network. 2.The wireless power transfer primary resonant network as claimed in claim1 wherein the reactive tuning component is selected dependent on a givenvariation in coupling between the primary and secondary resonantnetworks.
 3. The wireless power transfer primary resonant network asclaimed in claim 1 wherein the reactive tuning component is selected toconstrain the variation in reactive loading on the power supply.
 4. Thewireless power transfer primary resonant network as claimed in claim 1wherein the reactive tuning component is selected to constrain the powerfactor.
 5. The wireless power transfer primary resonant network asclaimed in claim 1 wherein the tuning component comprises the primarywinding.
 6. The wireless power transfer primary resonant network asclaimed in claim 1 wherein the given variation in inductance orcapacitance is caused by relative movement or displacement of a pick-upwinding of the secondary resonant network relative to the primarywinding.
 7. The wireless power transfer primary resonant network asclaimed in claim 2 wherein the given variation in coupling is caused byrelative movement of a pick-up winding of the secondary resonant networkrelative to the primary winding.
 8. A wireless power transfer secondaryresonant network including: a pick-up winding capable of receivingenergy from a varying magnetic field produced by a primary resonantnetwork; and at least one reactive tuning component selected toconstrain the reactive loading on a power supply which energises theprimary resonant network, the reactive tuning component being selecteddependent on a given variation in inductance or capacitance of thesecondary resonant network and a given variation in inductance orcapacitance of the primary resonant network to which the secondaryresonant network is coupled.
 9. The wireless power transfer secondaryresonant network as claimed in claim 8 wherein the reactive tuningcomponent is selected dependent on a given variation in coupling betweenthe primary and secondary resonant networks.
 10. The wireless powertransfer secondary resonant network as claimed in claim 8 wherein thereactive tuning component is selected to constrain the variation inreactive loading on the power supply.
 11. The wireless power transfersecondary resonant network as claimed in claim 8 wherein the reactivetuning component is selected to constrain the power factor.
 12. Thewireless power transfer secondary resonant network as claimed in claim 8wherein the tuning component comprises the pick-up winding.
 13. Thewireless power transfer secondary resonant network as claimed in claim 8wherein the given variation in inductance or capacitance is caused byrelative movement or displacement of the pick-up winding relative to aprimary winding of the primary resonant network.
 14. The wireless powertransfer secondary resonant network as claimed in claim 8 wherein thegiven variation in coupling is caused by relative movement of thepick-up winding the pick-up winding relative to a primary winding of theprimary resonant network.
 15. An apparatus for wireless power transferincluding: a primary resonant network, and a secondary resonant networkcoupled to the primary resonant network, wherein the apparatus has asystem operating frequency and one or both of the primary resonantnetwork and the secondary resonant network have a natural resonantfrequency that is different from the system operating frequency, andwherein the natural resonant frequency of the primary resonant networkis selected dependent on a given variation in inductance or capacitanceof the primary resonant network and a given variation in inductance orcapacitance of the secondary resonant network.
 16. The apparatus asclaimed in claim 15 wherein the natural resonant frequency of theprimary resonant network is selected dependent on a given variation incoupling between the primary and secondary resonant networks.
 17. Theapparatus as claimed in claim 15 wherein the natural resonant operatingfrequency of the primary resonant network is selected to constrain avariation in the operating frequency of the primary resonant network.18. The apparatus as claimed in claim 15 comprising a wireless powertransfer charger.